From magnetic order to quantum disorder: a $\hat{I}¼$SR study of the Zn-barlowite series of $S=\frac{1}{2}$ kagomé antiferromagnets, Zn${}_x$Cu${}_{4-x}$(OH)${}_6$FBr

Abstract

We report a comprehensive muon spectroscopy study of the Zn-barlowite series of $S=\frac{1}{2}$ kagomé antiferromagnets, Zn${}_x$Cu${}_{4-x}$(OH)${}_6$FBr, for $x=0.00$ to $0.99(1)$. By combining muon spin relaxation and rotation measurements with state-of-the-art density-functional theory muon-site calculations, we observe the formation of both $\hat{I}¼$--F and $\hat{I}¼$--OH complexes in Zn-barlowite. From these stopping sites, implanted muon spins reveal the suppression of long-range magnetic order into a possible quantum spin liquid state upon increasing concentration of Zn-substitution. In the parent compound ($x=0$), static long-range magnetic order below $T_{\mathsf{N}}=15$ K manifests itself in the form of spontaneous oscillations in the time-dependent muon asymmetry signal consistent with the dipolar fields expected from the calculated muon stopping sites and the previously determined magnetic structure of barlowite. Meanwhile, in the $x=1.0$ end-member of the series---in which antiferromagnetic kagomé layers of Cu${}^{2+}$ $S=\frac{1}{2}$ moments are decoupled by diamagnetic Zn${}^{2+}$ ions---we observe that dynamic magnetic moment fluctuations persist down to at least 50 mK, indicative of a quantum disordered ground state. We demonstrate that this crossover from a static to dynamic magnetic ground state occurs for compositions of Zn-barlowite with $x>0.5$, which bears resemblance to dynamical behaviour of the widely studied Zn-paratacamite series that contains the quantum spin liquid candidate herbertsmithite.

11 pages, 5 figures, supplementary information